scholarly journals The basic reproductive number and particle-to-plaque ratio: comparison of these two parameters of viral infectivity

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Winston McCormick ◽  
Leonard A. Mermel

AbstractThe COVID-19 pandemic has brought more widespread attention to the basic reproductive number (Ro), an epidemiologic measurement. A lesser-known measure of virologic infectivity is the particle-to-plaque ratio (P:PFU). We suggest that comparison between the two parameters may assist in better understanding viral transmission dynamics.

2019 ◽  
Vol 27 (1) ◽  
pp. 241-266
Author(s):  
FABIO SANCHEZ ◽  
JORGE ARROYO-ESQUIVEL ◽  
PAOLA VÁSQUEZ

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, R0, is computed, as well as a sensitivity analysis on R0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.


2014 ◽  
Vol 07 (01) ◽  
pp. 1450006 ◽  
Author(s):  
STEADY MUSHAYABASA ◽  
CLAVER P. BHUNU

Hepatitis C virus (HCV) is a blood-borne infection that can lead to progressive liver failure, cirrhosis, hepatocellular carcinoma and death. A deterministic mathematical model for assessing the impact of daily intravenous drug misuse on the transmission dynamics of HCV is presented and analyzed. A threshold quantity known as the reproductive number has been computed. Stability of the steady states has been investigated. The dynamical analysis reveals that the model has globally asymptotically stable steady states. The impact of daily intravenous drug misuse on the transmission dynamics of HCV has been discussed through the basic reproductive number and numerical simulations.


2011 ◽  
Vol 140 (3) ◽  
pp. 554-560 ◽  
Author(s):  
A. F. HINCKLEY ◽  
B. J. BIGGERSTAFF ◽  
K. S. GRIFFITH ◽  
P. S. MEAD

SUMMARYPlague is thought to have killed millions during three catastrophic pandemics. Primary pneumonic plague, the most severe form of the disease, is transmissible from person-to-person and has the potential for propagating epidemics. Efforts to quantify its transmission potential have relied on published data from large outbreaks, an approach that artificially inflates the basic reproductive number (R0) and skews the distribution of individual infectiousness. Using data for all primary pneumonic plague cases reported in the USA from 1900 to 2009, we determined that the majority of cases will fail to transmit, even in the absence of antimicrobial treatment or prophylaxis. Nevertheless, potential for sustained outbreaks still exists due to superspreading events. These findings challenge current concepts regarding primary pneumonic plague transmission.


2008 ◽  
Vol 16 (04) ◽  
pp. 519-529 ◽  
Author(s):  
XIAOWEI WANG ◽  
JIE LOU

Our models characterize the transmission dynamics of rabies between human and dogs. Firstly, we build an ODE model to represent the natural spreading of rabies in dogs and human. We get the basic reproductive number R0 and the global stability for both the disease-free equilibrium and the endemic equilibrium. Then, we build a controlling model for rabies. We compare the efficiency of three strategies for controlling the rabies: culling, vaccination, culling and vaccination, and get controlling thresholds for different strategies. The results of analysis and simulations indicate that vaccination is the best choice and culling is the worst one to control rabies. Vaccination on dogs in cities and culling and vaccination on dogs in rural areas of China are recommended for controlling rabies. Our study provides a theoretical basis for controlling rabies in China.


Author(s):  
Longxiang Su ◽  
Na Hong ◽  
Xiang Zhou ◽  
Jie He ◽  
Yingying Ma ◽  
...  

ABSTRACTUnderstanding the transmission dynamics of COVID-19 is crucial for evaluating its spread pattern, especially in metropolitan areas of China, as its spread can lead to secondary outbreaks outside Wuhan, the center of the new coronavirus disease outbreak. In addition, the experiences gained and lessons learned from China have the potential to provide evidence to support other metropolitan areas and large cities outside China with emerging cases. We used data reported from January 24, 2020, to February 23, 2020, to fit a model of infection, estimate the likely number of infections in four high-risk metropolitan areas based on the number of cases reported, and increase the understanding of the COVID-19 spread pattern. Considering the effect of the official quarantine regulations and travel restrictions for China, which began January 23∼24, 2020, we used the daily travel intensity index from the Baidu Maps app to roughly simulate the level of restrictions and estimate the proportion of the quarantined population. A group of SEIR model statistical parameters were estimated using Markov chain Monte Carlo (MCMC) methods and fitting on the basis of reported data. As a result, we estimated that the basic reproductive number, R0, was 2.91 in Beijing, 2.78 in Shanghai, 2.02 in Guangzhou, and 1.75 in Shenzhen based on the data from January 24, 2020, to February 23, 2020. In addition, we inferred the prediction results and compared the results of different levels of parameters. For example, in Beijing, the predicted peak number of cases was approximately 466 with a peak time of February 29, 2020; however, if the city were to implement different levels (strict, mild, or weak) of travel restrictions or regulation measures, the estimation results showed that the transmission dynamics would change and that the peak number of cases would differ by between 56% and ∼159%. We concluded that public health interventions would reduce the risk of the spread of COVID-19 and that more rigorous control and prevention measures would effectively contain its further spread but that the risk will increase when businesses and social activities return to normal before the end of the epidemic. Besides, the experiences gained and lessons learned from China are potential to provide evidences supporting for other metropolitan areas and big cities with emerging cases outside China.


2021 ◽  
Vol 47 (4) ◽  
pp. 1464-1477
Author(s):  
Seleman Ismail ◽  
Adeline Peter Mtunya

Ebola virus (EBOV) infection is a hemorrhagic and hazardous disease, which is among the most shocking threats to human health causing a large number of deaths. Currently, there are no approved curative therapies for the disease. In this study, a mathematical model for in-vivo Ebola virus transmission dynamics was analyzed. The analysis of the model mainly focused on the sensitivity of basic reproductive number,  pertaining to the model parameters. Particularly, the sensitivity indices of all parameters of  were computed by using the forward normalized sensitivity index method. The results showed that a slight change in the infection rate immensely influences  while the same change in the production rate of the virus has the least impact on . Thus, , being a determining factor  of the disease progression, deliberate control measures targeting the infection rate, the most positively sensitive parameter, are required. This implies that reducing infection rate will redirect the disease to extinction. Keywords: Ebola virus infection, immune response, sensitivity index, mathematical model.


2011 ◽  
Vol 04 (03) ◽  
pp. 329-346 ◽  
Author(s):  
JUN-YUAN YANG ◽  
XIAO-YAN WANG ◽  
XUE-ZHI LI ◽  
FENG-QIN ZHANG

An age-structured epidemiological model for the disease transmission dynamics of TB is studied. We show that the infection-free steady state is locally and globally asymptotically stable if the basic reproductive number is below one, and in this case, the disease always dies out. We prove that the endemic steady state exists when the basic reproductive number is above one. In addition, the endemic steady state is globally asymptotically stable if the basic reproductive number is above one and death rate due to TB is zero.


2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Felix Okoe Mettle ◽  
Prince Osei Affi ◽  
Clement Twumasi

Mathematical models can aid in elucidating the spread of infectious disease dynamics within a given population over time. In an attempt to model tuberculosis (TB) dynamics among high-burden districts in the Ashanti Region of Ghana, the SEIR epidemic model with demography was employed within both deterministic and stochastic settings for comparison purposes. The deterministic model showed success in modelling TB infection in the region to the transmission dynamics of the stochastic SEIR model over time. It predicted tuberculosis dying out in ten of twelve high-burden districts in the Ashanti Region, but an outbreak in Obuasi municipal and Amansie West district. The effect of introducing treatment at the incubation stage of TB transmission was also investigated, and it was discovered that treatment introduced at the exposed stage decreased the spread of TB. Branching process approximation was used to derive explicit forms of relevant epidemiological quantities of the deterministic SEIR model for stability analysis of equilibrium points. Numerical simulations were performed to validate the overall infection rate, basic reproductive number, herd immunity threshold, and Malthusian parameter based on bootstrapping, jackknife, and Latin Hypercube sampling schemes. It was recommended that the Ghana Health Service should find a good mechanism to detect TB in the early stages of infection in the region. Public health attention must also be given to districts with a potentially higher risk of experiencing endemic TB even though the estimates of the overall epidemic thresholds from our SEIR model suggested that the Ashanti Region as a whole had herd immunity against TB infection.


Author(s):  
Robert C. Reiner Jr. ◽  
David L. Smith

A theory for the transmission dynamics and control of malaria was developed around a set of concepts, quantities, and mathematical models introduced by Ronald Ross. Decades later, Macdonald linked Ross's models to epidemiological and entomological data, developed the concept of the basic reproductive number, R0, and proposed a rudimentary theory of control based on sensitivity to parameters. Here, we review development of the Ross–Macdonald model, present one simple version, and provide an eclectic critique of the theory based on studies conducted more recently. While mosquito populations are logically necessary for mosquito-borne pathogen transmission, the study of transmission since then shows it is noisy, heterogeneous, and complex. Heterogeneity, stochasticity, and complexity represent important challenges for applying theory in context.


2018 ◽  
Vol 37 ◽  
pp. 39-50 ◽  
Author(s):  
Rafiqul Islam ◽  
Md Haider Ali Biswas ◽  
ARM Jalal Uddin Jamali

This study deals with transmission dynamics of novel influenza A (H1N1) virus to understand the evolution of its epidemic in Bangladesh. For this purpose an SEIR model has been employed to study the dynamics of A (H1N1) virus relating to data of Bangladesh. To find threshold conditions, the equilibria and stability of the equilibria of the model have been determined and also analyzed. Basic Reproductive Number (R0) is determined relating to data of Bangladesh by which Herd Immunity Threshold has been estimated. Our numerical result suggests that vaccinating 12.69% population of Bangladesh can control spread of the pandemic novel A (H1N1) virus when outbreak occurs.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 39-50


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